Cramer-von Mises Test for Normality
Performs the Cramer-von Mises test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 5.1.3).
CramerVonMisesTest(x)
x |
a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. |
The Cramer-von Mises test is an EDF omnibus test for the composite hypothesis of normality. The test statistic is
W = \frac{1}{12 n} + ∑_{i=1}^{n} ≤ft (p_{(i)} - \frac{2i-1}{2n} \right),
where p_{(i)} = Φ([x_{(i)} - \overline{x}]/s). Here, Φ is the cumulative distribution function of the standard normal distribution, and \overline{x} and s are mean and standard deviation of the data values. The p-value is computed from the modified statistic Z=W (1.0 + 0.5/n) according to Table 4.9 in Stephens (1986).
A list of class htest, containing the following components:
statistic |
the value of the Cramer-von Mises statistic. |
p.value |
the p-value for the test. |
method |
the character string “Cramer-von Mises normality test”. |
data.name |
a character string giving the name(s) of the data. |
Juergen Gross <gross@statistik.uni-dortmund.de>
Stephens, M.A. (1986) Tests based on EDF statistics In: D'Agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.
Thode Jr., H.C. (2002) Testing for Normality Marcel Dekker, New York.
shapiro.test for performing the Shapiro-Wilk test for normality.
AndersonDarlingTest, LillieTest,
PearsonTest, ShapiroFranciaTest for performing further tests for normality.
qqnorm for producing a normal quantile-quantile plot.
CramerVonMisesTest(rnorm(100, mean = 5, sd = 3)) CramerVonMisesTest(runif(100, min = 2, max = 4))
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